Find the Laplace transform of \(\left\{ {{e^{ - t}}\mathop \smallint \limits_0^t \frac{{\sin t}}{t}dt} \right\}\)

1
\(\frac{1}{{s + 1}}{\cot ^{ - 1}}\left( {s + 1} \right)\)
2
\(\frac{1}{s}{\tan ^{ - 1}}\left( {s + 1} \right)\)
3
\(\frac{1}{{s + 1}}{\tan ^{ - 1}}\left( {s + 1} \right)\)
4
\(\frac{1}{s}{\cot ^{ - 1}}\left( {s + 1} \right)\)

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